Isotensoid structure



Feb. 18, 1964 H. u. SCHUERCH ISOTENSOID STRUCTURE 3 Sheets-Sheet 1 Filed Dec. 14, 1959 ,Hiws U. SCHUEQC/L 17v vEA/rae 5g #1 :5 Abram/1:315 1122915, 107554, Roses @Ifeem Feb. 18, 1964 H. u. SCHUERCH zsomusom STRUCTURE 3 Sheets-Sheet 2 Filed Dec. 14, 1959 Jiiws U. 50/0590;

, JM EMm/Q. B Ms A 770,?4/555 Ewe/s, hscfg B95554; .HEEM

1954 H. u. SCHUERCH ISOTENSOID STRUCTURE 3 Sheets-Sheet 3 Filed Dec. 14, 1959 w M M jlj/vs UT Sam/520M, l'ivvewrak.

5 A45 firmewzys, ,Himms, did/saw, Buses (ii-Kean United States Patent 3,121,451 ISOTENSSID STRUCTURE Hans U. Sehuerch, 73 t Arholado Road, Santa Barbara, Calif. Filed Dec. 14, 1959, Ser. No. 859,473 38 Claims. (U. 150-.5)

My invention relates to the filamented bodies, such as hollow vessels of minimum weight per enclosed volume having maximum strength-toweight ratios.

The invention comprehends filamented bodies in which filamentary reinforcements carry substantially all of the primary structural loads, these filaments being wires, threads, yarns, ropes, etc., either singly or in multiple arrays. Such filaments may or may not be bonded together by or embedded in a matrix of some difierent material filling the voids between individual filaments. Most commonly the filaments are joined or covered by a matrix material but this material serves secondary functions only, e.g., bonding or spacing of the filaments, sealing and crack barrier formation, load redistribution in case of partial failure, prevention of filament buclding in case of compressive loads, etc.

t is an object of the invention to provide a filamented structure in which the tensile or compressive force along each filament is both uniform and invariant throughout its length within close limits and in which no shearing force transfer through the matrix is required. The term isotensoid aptly describes such structures and it is an object of the invention to provide isotensoid structures of various shapes, including for instance for pressure vessels shapes bounded by surfaces of topological genus l, genus 2 or higher, which structures are able to withstand or transmit structural loads and are capable of undergoing deformations without impairment of structural integrity, e.g., Without impairment of such primary functions as load bearing, load transmitting, etc., and without impairment of such secondary functions as forming pressuretight barriers, separating dissimilar fiuids, controlling heat transfer between fluid media, etc.

ideally, the invention employs essentially endless filaments by which I have reference to lengths or configurations in which the filament may return one or several times on a on rvitious path into the vicinity of its beginning or end. The term thus includes filaments forming end loops or ti ht spirals. Essentially endless filaments may be single or multiple strand, the latter including a plurality of individual fibers which may be relatively short but which are held together as a part of the filament by mutual friction or bonding.

By utilizing filaments to resist the load and by relating shape to loads as will be described it becomes possible to stress all filaments substantially uniformly and equally at values just short of their breaking stresses. If the filaments are of uniform cross section and strength it thus becomes possible to obtain minimum-weight structures. If the invention is applied to pressure vessels the filamentary nature of the structure also may prevent explosive or catastrophic failure upon puncture because the matrix material may form an effective barrier against crack propagation. Also it becomes possible by use of the invention to make, if desired, collapsible structures that can be stored in small spaces and inflated to predetermined shape. It is an object of the invention to provide structures having high strength-to weight ratios yet which are insensitive to catastrophic crack propagation and which, if desired, can be made collapsible into small spaces.

Many extremely small filaments show remarkable strength. Thin filaments of glass, refractory fibers and filamentary crystals may have strengths of the order of "ice 10 psi. A substantial percentage of the filament strength can be retained by proper design. While it has previously been proposed to reinforce plastic structures or vessels with filamentary material, a review of the structural performance thereof shows that usually less than 50% of the potential material strength is exploited. It is an object of the present invention to provide design relationships through which it is possible to utilize practically all of the potential material strength of filamentary materials. Other objects of the invention reside in the provision of uniquely shaped structures as hereinafter suggested.

Still further objects and advantages of the invention will be evident to those skilled in the art from the following descriptions of exemplary embodiments and the accompanying drawings.

Referring to these drawings:

FIG. 1 represents a series of curves resulting from solutions of one of the isotensoid equations used in the invention;

FIG. 2 is a diagrammatic perspective view of one embodiment of the invention with a section cut away for better illustration;

FIGS. 3 and 4 are diagrammatic perspective views of two toroidal embodiments having doubly connected volumes and the same topology;

FIG. 5 is a perspective view of an embodiment having a doubly connected volume the aXis of which is not in a single plane;

FIGS. 6 and 7 are diagrammatic perspective views of two other embodiments;

FIG. 8 is a fragmentary cross-sectional view of a multilayer structure illustrating how multi-fiber filaments can be shaped and held together;

FIG. 9 is a diagrammatic view illustrating mechanism by (which the embodiment of FIG. 7 or other embodiments can be formed;

FIG. 10 is a perspective view of a winding form useful in conjunction with the machine of FIG. 9; and

FIG. 11 is a diagrammatic view suggesting steps that can be used in producing the embodiment of FIG. 9.

An endless filament of an isotensoid body forming essentially a closed loop can be defined with reference to any point s on the center line of the filament by the vector 5 from the origin of an arbitrary coordinate system to the point s. A summation of such vectors can define a three dimensional structure the surface of which is bounded by such filaments disposed side-by-side. In the most general relationship in which the load is not necessarily uniform at different positions along the surface, it has been determined that isotensoid relationships will result from a structure having filaments of a geometrical configuration Erelated to a volumetric load factor p (representing the load from external sources applied to a unit volume of the structure) by substantially the equation:

(Z 5 I p 234, 2 i 1) where:

k=the number of filaments permeating a unit volume around point 8,

t =the force in any such filament at any point between attachments thereof other than attachments to any matrix,

ds=a small (difrerential) length along the path of a filament,

=the unit vector parallel to the tangent to the filads ment at point s, and

(hf-d8 d8 -the second derivative of the vector 5 The second derivative of the vector .5 describing the space curve of a filament path is again a vector. This vector is parallel to the radius of curvature of the space curve and is equal in magnitude to the curvature of the space curve. The unit volume referred to above has reference to a space occupied by filaments of unit length.

The mathematical relationship between load and filamentary geometry given in Equation 1 is exactly satisfied only for ideal structures consisting of filaments without internal friction and Without any restraining matrix material. In practice such conditions cannot be satisfied with mathematical precision. The isotensoid structures of the invention substantially satisfy by the above Equation 1, in the sense that deviations should not exceed the following: As to the force or load in each filament between attachments, this should be within the range of .9-1.1r. The configuration should be such that the tangent angle at any point thereon should vary from the true tangent angle by not more than of a radian (approximately 1 angular degree). 'If a matrix material is employed, it should never carry more than of the internal forces generated by external loads. In other words, in a pressure vessel for example at least 90% of any internal forces induced by pressure loads should be carried by the filaments.

The texture of an isotensoid body is given by the geometry of the filamentary paths that permeate the body. In the most general form of the invention, these paths may be completely at random, restrained only by the condition that Equation 1, relating volumetric loads and filamentary geometry, remain satisfied. In other forms to be described the filamentary paths are geodesic or meridional.

A particularly important application of the isotensoid structures of the invention is in the field of onionoid hollow pressure vessels characterized by loads that are normal to the surface of the structure. These may be bodies of revolution with rotational symmetry with respect to the z axis and with filaments arranged geodesically. The loads on these bodies may be an internal pressure normal to the internal surface of the body. This pressure p may be exerted by a contained gas, a contained liquid and/or by adjoining structural components. On the assumption that the internal pressure p may vary along the z axis albeit in a pattern rotationally symmetrically distributed, all points in the mid-surface halfway between the outer and inner surfaces of an ideal isotensoid hollow vessel will substantially satisfy the equations:

where r=radius to any point on any meridian of said midsurface measured perpendicular to the z axis,

t=tensile force in filament,

n=number of filaments traversing a cross section,

B=helix angle between the geodesics and a corresponding meridian, and

B =-and r are arbitrary integration constants.

As before, isotensoid structures substantially satisfying Equations 2 and 3 are contemplated by the invention. Matrix materials, if used, should not carry more than 10% of the internal forces generated by external loads and the actual tensile force in each filament of the vessel should differ within the filament and from the tensile force in other filaments Within a range no greater than .9-1.1t.

In the special case under consideration, the filamentary geometry describes lines that are geodesics for the onionoid surface of the pressure vessel. Excessive buildup at or near the poles with helix angles other than zero is avoided in ways to be described, e.g. making the structure with pole openings which can be closed by separate elements made of conventional design or by use of the isotensoid principles of the invention.

If r and 5 are defined respectively as the radius and the helix angle at the equator the minimum radius controlling the size of any pole opening will be uniquely defined. An isotensoid body of revolution using geodesic winding patterns of a helix angle different from zero and shaped in accordance with Equations 2 and 3 will always have two polar openings of equal size and the equatorial helix angle .6 will be uniquely defined by the ratio of the equatorial diameter to the required diameter of the polar opening.

In the even more specific case where {3:0, i.e. where the geodesics are meridional, the mid-surface can be more simply defined. In this special case Equations 2 and 3 may be simplified to:

=0 d 2 3/2 1+ where:

As before, Equation 4 would delineate an isotensoid structure with mathematical precision. The isotensoid structures of the invention conform substantially to Equation 4 in the special case under consideration, deviations being no greater than set forth above as concerns Equations 2 and 3.

Solutions of all of the Equations 1, 2, 3, or 4 cannot be expressed in closed form. A number of solutions for Equation 4 for the special case where p is uniform are shown schematically in FIG. 1 of the drawings. The outer portion of curve 10, for example, corresponds generally to the cross sectional configuration of the isotensoid structure of FIG. 2. Likewise the looped or closed portion 12a of curve 12 approximately outlines the cross section of the embodiment of FIG. 3.

Referring more specifically to FIG. 2, the hollow isotensoid structure 14 therein shown includes a multitude meridional filaments 15 only a few of which are suggested. These are anchored to rings 16 and 17 with their intersupport portions connected, if at all, by a matrix material 18 which serves primarily to retain the spacing of the filaments. The loads are taken by the filaments and are represented by isotensile stresses in the filaments as previously described. The function of the matrix material is primarily to maintain the filaments in the desired predetermined position. The shape of the structure is made in accordance with Equation 4 supra. The openings of the rings 16 or 17 may provide access to or from the interior space 19 or may be partially or completely closed by supplementary structures made in accordance with the invention or otherwise. Typical supplementary structures will be later exemplified.

The meridional filaments 15 are anchored to the rings 16 and 17 in any suitable way. There may be some overlap of the filaments at the rings to build up a somewhat thicker area which may assist the connection of structures that partially or completely close the corresponding opening. However it is preferable to avoid such overlap and to minimize or eliminate differences in spacing of the filaments near the rings as compared with near the equator. One excellent way of accomplishing the latter is to make each filament wide and thin (flat) in cross section at the equator, tapering to a cross section that is narrow and thick toward the poles. if the filament is made up of numerous bundled fibers the spacing thereof within the lament may remain essentially uniform. It is not essential to the invention that wall thickness be uniform throughout and the use of such filaments tapering in cross section between inner and outer positions or loci is not limited to the isotensoid design determined by substantial adherence to the above equations.

FIG. 3 illustrates another embodiment that is designed in accordance with Equation 4. Here the vessel Ztl is shown in an initial substantially toroidal shape but of a cross sectional shape corresponding to the portion 12a of curve 12 of FIG. 1. The outer portion 21 of the cross section is rather rounded as compared with the more sharply curved inner portion 22. The latter is reinforced circumferentially or equatorially by any suitable ring 25 which forms a second filamentary system similar in function to the rings 15 and 17 of FIG. 2. Filaments 26 (only a few of which are shown in FIG. 3) are in one of two general forms. As illustrated, they are meridional endless rings in planes radial to the central or z axis zz and are linked with the ring 25, being sometimes compacted thereadjacent as compared with a position at the crest of the outer portion 21, the compaction being either to a compact side-by-side relation or an over-la ping relation as previously mentioned. However filament spacing adjacent the ring 25 and the crest of the outer portion 21 may be uniform by using the varying cross section of the filament as described with reference to FIG. 2. Such filaments may be initially endless or may be made endless by joining the ends of individual filaments to the ring 25. Alternately, the filaments 2% may be essentially endless rings by being composed of respective turns of a long length of filamentary material wound in a general helical path around the ring 25 in closely spaced turns of the desired peripheral length. The helix angle can be so small as to be of negligible significance if the turns are tightly compacted at the inner portion 22.

In this embodiment if any matrix material 28 is utilized its function will be primarily to maintan the filaments 26 appropriately spaced. Loads inside the vessel will be taken by the filaments and will develop isotensile forces therein substantially equal in each filament at positions beyond the support formed by the ring 25 and sub stantially equal as between the different filaments.

Structures in which the filaments are turns of a long length of filamentary material are particularly useful in some instances and need not employ the ring 25. Typical forms are shown in H68. 4 and 5, the latter being shaped as determined by Equation 1 and the former being shaped in accordance with Equations 2 and 3 providing for rotational symmetry. FIG. 4 illustrates a toroidal vessel bounded by a surface of genus 2 considering the usual ingress opening or by two surfaces of genus 1 in the absence of such ingress opening and providing a doubly connected volume the axis of which is shown in a single plane. If deformation out of such plane is to be avoided upon change in internal pressure two systems of filaments are employed, composed of filaments 29 and 3t? successively wound in different layers at helix angles that are equal at corresponding points but opposite in sign, the helix angle 5 being determined by Equations 2 and 3 and being different at inner and outer portions of any cross section, being larger toward the inner portion than toward the outer portion. Any initial space between turns of each filament system may be filled in by later turns of the same filament system, the turns being joined by a matrix 31 as previously described. The embodiment of FIG. 4 with its crossing filaments eliminates the need for a ring 25, as used in FIG. 3. Additionally the crossed filaments make the structure stay flat upon change in pressure with its axis in substantially a single plane so that it retains a rotational symmetry about the z axis. The cross section of the P16. 4 embodiment is somewhat egg shaped with its inner portion more blunt than its outer portion.

In H6. 5 a single length of filamentary material is wound helically to form filaments or turns 32. shaping a doubly connected volume. Here the closed axis is not in a single plane but is of a general figure eight form spaced a diameter or more at the crossover point. The filament at no place crosses another turn in this embodiment, which can be wound either in substantially the ultimate figure eight form shown or with its closed axis forming a circle and later twisted into its ultimate form as by change in internal pressure. As before, the helix angle 8 is different at the inner and outer portions of a cross section as determined by Equation 1. A matrix material 33 may bridge or join the filaments 32, only a portion of the latter being illustrated in FIG. 5 and a reinforcing ring similar to of FlG. 3 can be employed to lie along corresponding portions of the various cross sections of the structure.

FIG. 6 illustrates a hollow vessel 34 having a main por tion 35 with end openings as and 37 partially closed by supplementary structures including a closure member 38 and a ring element 39. The main portion 35 is of filamented construction in which a long filamentary member is wound substantially helically to form filaments 40. The filaments lie substantially tangential to the openings 36 and 37 at positions thereadjacent.

The ring element 39 may be any separately formed member adhered within the opening 37. It preferably includes a flange 41 lying immediately within the opening 37 along the inner surface of the main portion 35, being suitably adhered thereto. The ring element 39 includes a neck portion i2 which may extend through the opening 37 to other supplementary structures closing or partially closing the opening.

Similarly, the closure member 38- carries a flange 43 conforming to the inner surface of the main portion 35 adjacent the opening as. A neck portion 44 extends through the opening and in this embodiment is closed by a domed portion 45. If desired this domed portion may be of filamented construction shaped in accordance with one of the aforesaid equations or it may be of conventional form made of metal or any other suitable material. The necks and flanges of the ring 39 and the closure member 3!; may anchor the filaments so, which are otherwise free between such supports except as they may be joined by a matrix material The shape of the interface between each flange ll, 43 and the corresponding annulus of the main portion 35 warrants separate consideration albeit the portions between the interface areas will be shaped in accordance with Equations 2 and 3 with helical geodesc' The shape of the vessel in each such annulus should take into consideration the pressure exerted by the flange bearing thereon. The otherwise pertinent Equations 2 and 3 should be modified by substituting for the internal pressure p the interface pressure, i.e., the pressure exerted by the flange bearing on the pressure vessel shell, the resulting modified equation being used to determine the shape of each annulus that is to become an interfacial area.

In FIG. 7 is shown a vessel made of meridional filaments 51 anchored in a somewhat different manner, the shape of the vessel between the interfacial zones being in accordance with Equation 4, the interfacial zones being shaped as suggested with reference to FlG. 6. In FIG. 7 the lower and upper openings are respectively formed or determined by rings 53 and 54 around which the filaments are looped. Two sidc-by-side filaments 51 may be respective halves of an endless filament looped around the rings 53 and 541. Alternatively, such adjacent or side-byside filaments 51 may be halves of one of a number of turns of filamentary material wound around and between the rings 53, 54 in the manner exemplified in FIGS. 9 and 10 to be described.

The opening defined by the ring 54 may receive a ring element 57 having a collar 58 to which a flange 59 is connected, the latter fitting the annulus of the internal surface of the vessel 56 in the vicinty of the ring 54. Similarly, the opening formed by the ring 53 is closed by a closure member 60 having a flange 62 fitting and adhered to an annulus of the internal surface of the vessel adjacent the ring 53.

Structures as hereinbefore exemplified can be constructed in various ways and by use of various materials. Some of the general considerations will be discussed before exemplifying one specific Way of formulating a vessel.

The filaments with which the invention is concerned may be individually homogeneous, constituting a single extruded glass fiber for example, or each filament may comprise many individual fibers woven or twisted together into filamentary form and retained in such form either by friction or adhesion. Glassy or crystalline filaments are examples of the high-strength materials that can be employed.

The invention comprehends monolayer or polylayer vessels. The latter are often desirable as pressure vessels in which the filamentary materials are required to absorb strains both in an axial direction along the direction of the filaments and in a direction perpendicular thereto. That is to say materials for this purpose must exhibit satisfactory transverse compliance charcteristics. Such a material may be produced by employing stranded filaments in which the individual fibers are bonded together with a relatively strong and hard or non-yielding susbtance, the filaments often being in a polylayer configuration.

The arrangement of material suggested by the crossseotional fragment of FIG. 8 is particularly useful in these connections. I-Iere several filaments 64 are shown, each formed of a large number of fibers 65 bonded together by a relatively strong and hard or nonyielding material 66 such as a suitable synthetic resin. Each filament may be a plastic impregnated roving in which long glass fibers are held together by a suitable resin. However, the resulting filaments 64 are themselves joined by a relatively soft or yielding material 67 acting as a matrix. The natural nesting tendency of the multi-fiber filaments 64 will, if the adjacent filaments are properly spaced and tensioned, tend to produce a diamond or parallelogram pattern conductive to transverse compliance of the composite material. If desired, there may be some initial shaping of the cross-section of the filaments to accentua-te this diamond pattern effect. If the material of FIG. 8 is subjected to biaxial strains, e.g. due to transverse expansion under internal pressure in any of the vessels of the invention, then the diamond shape of the filaments allows a transverse elongation by shearing or slipping motion of the soft matrix material filling the voids between the filaments.

In practice a material of the type shown in FIG. 8 can be produced by the standard procedures employed in the fabrication of glassdilament-wound plastic-bonded articles from resin-impregnated roving if the additional step is introduced of coating the pre-impregnated roving with a modified or flexibilized resin by use of rollers, spray guns or other coating means employed to add the coating before winding the roving in place. A hard modification of the same resin canbe used for the preimpregnation of the roving. Partial polymerization (B-staging) of the original resin may be used to avoid excessive mixing with the secondary coating of flexibilized resin.

The Winding or placement of the filaments should be precise. If these filaments consist of successive turns of a filamentary member Wound with a helix angle to fulfill the conditions of Equations 2 and 3, the angle of each successive turn should differ minutely from its neighbors, \as compared with any procedure in which a series of successive turns are built up in parallel planes as a band before the winding operation is shifted to another position wherein a second series of successive turns Will build up a second band shifted angularly from the first. Substantially stronger and better structures result from continual motion during the winding operation so that no two successive turns are in identical planes.

Two filaments disposed side-by-side should be capable of some relative longitudinal motion. That is to say, any restraint on the movement of a filament by its neighbor or by any matrix joining them should not prevent that degree of relative movement that will permit each to as sume its proportion of the load or to shift longitudinally to substantially equalize its load throughout its length. At the same time, lateral spreading of adjacent filaments should be restrained and this can be accomplished by the matrix material or by an equatorial member that will space the filaments while permitting some longitudinal movement of any filament relative to the equatorial member.

In instances where pressure vessels are to be produced it is usually desirable to employ a matrix material although filaments compacted in side-by-side relationship may be utilized to form certain vessels or bodies. In practice, some matrix material is desirable if for no other reason than to hold the filaments against lateral displacement from their desired positions.

The matrix largely determines the toughness and the flexibility of the structure and should be made of a relatively compliant matrix material. It is often practical to apply the matrix material during the winding, either simultaneously with the filaments or previously applied thereto. For example, glass fibers impregnated with polyester or epoxy resins can be wound, the curing being inhibited at this stage and completed only when the structure is complete. In other instances, the matrix material can be applied to newly-wound filaments whether wound in the ultimate shape or in a preliminary shape that can be made to deform into the ultimate shape.

The matrix material will desirably bridge across any spaces between adjacent filaments. However, the bridge will not be sufficiently long to permit the compliant matrix material to rupture or be displaced by the pressure load. Speaking quantitatively, the matrix material should never be required to carry more than 10% of the load, it being desirable that the filaments carry 90% or preferably susbtantially more of the load.

The matrix material in the structure may either surround or merely touch the filaments. In other words, the filaments can be considered as permeating a matrix material or the latter may be more of a layer disposed on one side of the filaments and held in position thereby. An example of the latter would be a fluid tight membrane of matrix or other material immediately inside the filaments of a pressure vessel and bonded thereto to prevent the aforesaid lateral displacement of the filaments while permit-ting those small longitudinal movements of filaments that are desirable in equalizing the tension throughout the length thereof and equalizing tensions in adjacent filaments.

The vessel of FIG. 7 can be manufactured by a sequence illustrated in FIGS. 9-11, using a modified ringshuttle winder and a mandrel-less cure procedure. The initial winding operation preferably utilizes a temporary holding fixture 78 illustrated in FIG. '10 in which the ultimate lower and upper rings 53 and 54 are held coaxially by temporary spacing elements 80 which space the rings a predetermined greater distance than in the ultimate vessel 50.

This tempoary holding fixture 78 is mounted in a winding machine, suggested in FIG. 9, in which grooved wheels 81 and 82 at different elevations peripherally journal and turn the rings 53 and 54 about the common axis. The temporary holding fixture 78 is thus turned slowly relative to a base 85 by any suitable drive means not shown.

A suitable ring-shuttle winding machine 86 winds the filamentary material in successive loops about the rings 53 and 54. This winding machine is shown as including an arcuate member 87 secured to the base 85 and carrying rollers 89 which peripherally journal a. ring 90 carrying any suitable shuttle 92 of conventional design. The filamentary material 93 is wound on the shuttle. As the ring 99 rotates during slow turning of the temporary holding fixture 78 the filamentary material 93 is wound substantially helically on the fixture in loops or turns that are each linked by the rings 53 and 54-. In a typical example, the filamentary material may be 'a dry or wet roving suitably impregnated with a resin. Flexibility of lay up is retained by inhibiting the cure of the resin system at this stage.

The temporary holding fixture 7 8 is then removed from the winding machine and the ring element 57 is inserted either by deformation of the ring 59 or the ring element 57 or by temporarily separating the meridional filaments to permit such insertion in a sidewise direction. The temporary spacing elements 89 are then removed by temporarily separating the meridional filaments adjacent thereto to permit such removal. After the filaments have returned to normal position they may be covered with a layer of thin flexible material. For example, the windings may be covered with a layer of meridional oriented tape of thin plastic such as Mylar (a thin polyester film material available in sheet or tape form) or other suitable material. At this stage it is usually desirable to insert the closure member 60 to close the opening adjacent the lower ring 53.

A temporary closure plate 96 is then suitably applied to the ring element 57 to close the lar e opening adjacent the ring 54-. A moderate fluid pressure P is then applied through an orifice 97 of the plate While the rings 53 and 54 are restrained only by the filaments. The vessel will expand into the desired vessel shape if the filaments are free to move relative to each other, each being free likewise to move longitudinally so as to equalize the stresses throughout. The spacing of the rings 53 and 54 may be adjusted to that desired in the ultimate vessel at this time. The vessel is then cured in its pressurized condition. A vacuum can be applied to remove trapped air from the filamented material prior to cure. A vacuum can also be applied to the curing zone around the unit during curing to remove volatile byproducts liberated during the curing of certain organic plastics.

The machine of FIG. 9 can be employed to wind the filaments of the toroidal form of FIGS. 3 or 4 or even the more complex form shown in FIG. 5. It is possible also to use other Winding equipment patterned to wind the filament in the desired manner.

LA wide variety of plastics useful in the practice of the invention are known. Synthetic resins are preferred. For example a resin known as Epon 828, a product of Shell Chemical Corp. will give good results. Additives and catalysts may be, for a hard modification, 40% Epon 815 and .5% benzyldimethyl amine or, for a flexible modification, 25% Thiokol LPS, a liquid polymer made by the Thiokol Corp. or any of a number of similar flexibilizers. Curing may be at about 300 F. for about three hours.

Various changes and modifications can be made without departing from the spirit of the invention as defined in the appended claims.

I claim as my invention:

1. A deformable isotensoid structure having a multiplicity of adjacent precisely-positioned filaments held in adjacent positions by a compliant matrix material carrying no more than 10% of the forces induced by external loads, the filaments carrying at least 90% of any forces induced by external loads applied to the structure, the

& p dS i where: w

t;=the axial force in any such filament at any point s therein between attachments thereof other than at tachments to said matrix,

k=the number of filaments permeating a unit volume around a point s,

ds=a small (differential) length along the path of a filament,

=the unit vector parallel to the tangent to the filad ment at point; 5, and

2 E =the second derivative of the vector 5 deviations from such equation covered by the above word substantially being no greater than the following: The force in each filament between such attachments being within the range .91.1 t, and the tangent angle at any point on the geometrical configuration varying from the true tangent angle by not more than & of a. radian.

2. An isotensoid structure as defined in claim 1 shaped as a vessel having a multiplicity of substantially-endless isotensoid filamentary turns wound as a toroid with said turns encompassing the closed longitudinal axis of the toroid, said turns being in said adjacent positions; a compliant matrix material holding said turns in said positions While permitting small relative movement of adjacent filaments; and a ring parallel to said closed longitudinal axis crossing all of said filamentary turns at corresponding positions thereof.

3. An isotensoid vessel as defined in claim 2 in which said ring links said filamentary turns and is positioned internally of said vessel.

4. An isotensoid structure as defined in claim 1 bounded by surfaces of the topological genus of a toroid providing a closed doubly connected volume having a closed longitudinal axis.

5. An isotensoid structure as defined in claim 4 in which said closed axis is of a general figure eight form having its crossover portions spaced from each other at least the distance across a cross-section of the structure.

6. A hollow isotensoid pressure vessel comprising an assemblage of geodesic filaments, said vessel having a midsurface that is substantially a surface of revolution with rotational symmetry With respect to the z axis and positioned halfway between the outer and inner surfaces of said hollow vessel, all points in said mid-surface s-ub stantially satisfyin the simultaneous equations:

r=radius to any point on any meridian of said mid-suriface measured perpendicular to the z axis,

p =internal pressure, which may vary along the z axis,

t=tensile force in filament,

n number of filaments traversing a cross section,

fizhelix angle between the geodesics and a meridian, and

[3 and r are arbitrary integration constants, the actual tensile force in each filament of said vessel differing within the filament and from the tensile force in other filaments within a range no greater than .9l.1t.

7. A hollow pressure vessel as defined in claim 6 including two pole openings spaced along the z axis, said mid-surface differing in diameter through a maximum between the pole openings as measured perpendicular to the z axis, said filaments being loops of a longer filamentary material wound in multiple turns bounding said pole openings, the angle of each successive turn differing from its neighbors.

S. A hollow pressure vessel as defined in claim 7 in which said pole openings are of equal size determined by making r and ,8 respectively the radius and the helix angle of the filaments at the equator of the vessel.

9. A hollow pressure vessel as defined in claim 7 in which said pole openings are of equal size, and including means for at least partially closing said pole openings.

10. A hollow pressure vessel as defined in claim 9 including a circular insert in each of said pole openings, each insert having a flange conforming to the inner surface of said pressure vessel and extending outwardly from said pole opening along such inner surface.

11. A hollow pressure vessel as defined in claim 6 bounded by a surface of topological genus 1, genus 2 or higher with a doubly connected volume having a closed longitudinal axis.

12. A hollow pressure vessel as defined in claim 11 including two overlying systems of helically wound filaments wound in opposite directions with the helix angle fl being different at inner and outer portions of any cross section of said vessel.

13. A hollow isotensoid pressure vessel comprising meridional filaments carrying at least 90% of an internal pressure load, said vessel having a mid-surface that is substantially a surface of revolution about the z axis, said mid-surface being halfway between the outer and inner surfaces of said vessel, all points in said mid-surface substantially satisfying the equation:

where 14. A hollow isotensoid pressure vessel as defined in claim 13 having two pole openings spaced from each other along the z axis and supplementary structures for at least partially closing each of said pole openings.

15. An isolated pressure vessel as defined in claim 13 having two pole openings spaced from each other along the z axis, said filaments being sections of a longer filamentary member wound as side-by-side loops, each loop forming two meridional filaments, the loops at said pole openings being closely packed.

16. An isotensoid pressure vessel as defined in claim 15 including a ring at each pole opening, both rings extending through each loop.

17. An isotensoid pressure vessel as defined in claim 16 in which said filamentary member is wound in advancing turns about said spaced rings, each turn being a loop forming two side-by-side meridional filaments of said vessel.

18. An isotensoid pressure vessel as defined in claim 15 including a circular insert in at least one of said pole openings having a flange conforming to the inner surface 1.2 of said vessel'adjacent such pole opening and extending outwardly therefrom along such inner surface.

19. An isotensoid pressure vessel as defined in claim 13 bounded by surfaces of the topological genus of a toroid providing a closed doubly-connected volume having a closed longitudinal axis.

20. An isotensoid pressure vessel as defined in claim 19 in which any cross section in a plane transverse to the longitudinal closed axis is of closed generally-oval shape with a rounded outer portion and a more sharply curved inner portion, each filament being a turn extending around such portions substantially in such plane.

21. An isotensoid pressure vessel as defined in claim 20 including a circumferential reinforcement ring at said more sharply curved portions of said cross sections substantially parallel to said closed longitudinal axis and linked with said filaments.

22. A pressure vessel comprising a plurality of endless side-by-side isotensoid substantially meridional filaments having the relation between load and filamentary geometry substantially satisfying Equation 1 said filaments looping outwardly from an inner locus through an outer locus and returning inwardly, the axes of such side-by-side filaments being closer together adjacent said inner locus than said outer locus, each filament being of a crosssectional shape varying along its length from a shape that is wide and thin adjacent said outer locus in directions respectively perpendicular to and along the inward-outward direction to a shape that is narrow and thick adjacent said inner locus, the difference in spacing of said filaments adjacent said inner and outer loci being substantially less than the spacing of their axes adjacent said loci, and a compliant matrix material holding said filaments in position and permitting small relative movement of said filaments, said matrix material carrying no more than 10% f the forces induced by external loads.

23. An isotensoid structure having a multiplicity of adjacent precisely-positioned filaments wound in a uniform pattern and having the relation between load and filamentary geometry substantially satisfying Equation 1, said filaments being held in adjacent positions by a compliant matrix material carrying no more than 10% of the pressure load, at least of the pressure load being .carried by the filaments.

24. An isotensoid structure as defined in claim 23 further characterized in that said matrix material is sufficiently compliant that adjacent filaments are capable of some relative longitudinal motion.

25. An isotensoid vessel bounded by surfaces of the topological genus of a toroid providing a closed doubly connected volume having a closed longitudinal axis, said surfaces being made of precisely-positioned endless isotensoid filaments sufiiciently close to each other to close the interior of said vessel and carry the pressure load on said surfaces.

26. An isotensoid vessel bounded by a surface of topological genus 1, genus 2 or higher with a doubly connected volume having a closed longitudinal axis, said surfaces being made of precisely-positioned endless isotensoid filaments having closely adjacent filament sections, and a compliant matrix material holding said filament sections in peripheral position, said matrix material carrying no more than 10% of the pressure load, at least 90% of the pressure load being carried by said isotensoid filaments.

27. An isotensoid vessel as defined in claim 26 in which said endless filaments are endless meridional rings.

28. An isotensoid vessel as defined in claim 26 in which said endless filaments are composed of respective turns of a long length of filamentary material wound in a generally helical path about said closed longitudinal axis in closely-spaced turns.

29. An isotensoid Vessel as defined in claim 28 in which the helix angle of said turns is sufficiently small to make such turns substantially meridional.

30. An isotensoid vessel as defined in claim 26 in which each filament comprises a large number of fibers and a hard substantially-nonyielding material bonding said fibers together to form said filament, said vessel having a peripheral polylayer wall providing said surfaces, each layer of said wall being made up of a plurality of said filaments held in adjacency by said compliant matrix material.

31. An isotensoid vessel as defined in claim 30 in which each filament is of a generally parallelogram shape in cross section.

32. An isotensoid vessel as defined in claim 26 including a ring parallel to said closed longitudinal axis crossing all of said endless filaments at corresponding portions thereof.

33. An isotensoid vessel as defined in claim 32 in which said ring links said filaments and is positioned in ternally of said vessel.

34. An isotensoid wessel as defined in claim 33 in which the outer portion of each cross section of the vessel in a plane perpendicular to said closed longitudinal axis is rounded, the inner portion of each such cross-section being more sharply curved at a position adjacent said ring.

35. An isotensoid structure having a boundary wall made exclusively of a multiplicity of immediately-adjacent endless substantially-isotensoid filaments wound in accordance substantially with Equation 1 and held in adjacent peripheral positions by a compliant matrix material carrying no more than of the pressure load, at least 90% of the pressure load being carried by said filaments.

36. An isotensoid structure as defined in claim 35 having a polylayer Wall, each filament comprising a large number of fibers and a hard substantially-nonyielding material bonding said fibers together to form such filament, each layer of said polylayer Wall being made up of a plurality of said filaments held in adjacency by said compliant matrix material.

37. An lsotensoid structure as defined in claim 36 in which each filament is of generally parallelogram shape in cross section.

38. An isotensoid structure as defined in claim 35 in the form of a vessel having a closed longitudinal axis traversing corresponding points within each cross-sectional plane that is perpendicular to such longitudinal axis, each endless filament being of varying cross-section tapering from a filament cross-section that is wide and thin in an equatorial zone of each such cross-sectional plane of said vessel to a cross-section that is narrow and thick at more polar positions in such cross-sectional plane, such thickness and thinness being measured along radial lines in such cross-sectional plane radiating from said longitudinal axis.

References Cited in the file of this patent UNITED STATES PATENTS 1,183,965 Fisher May 23, 1916 1,453,865 Dickinson et a1. May 1, 1923 1,468,496 Caldwell Sept. 18, 1923 1,622,787 Horton Mar. 29, 1927 1,928,640 Boardrnan Oct. 3, 1933 2,109,529 Goddard Mar. 1, 1938 2,119,518 Boardman June 7, 1938 2,224,274 Powers Dec. 10, 1940 2,633,172 Treiber Mar. 31, 1953 2,679,224 Sturdevant May 25, 1954 2,744,043 Rarnberg May 1, 1956 2,767,941 Gegner Oct. 23, 1956 2,843,153 Young July 15, 1958 2,848,133 Ramberg Aug. 19, 1958 FOREIGN PATENTS 120,088 Great Britain Oct. 25, 1918 261,427 Great Britain Feb. 10, 1927 UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No., 3 l2l 45l February 18,, 1964 Hans Un Schuerch It is hereby certified that error appears in the above numbered patent requiring correction and that the said Letters Patent should read as corrected below.

Column 3 lines 53 to 57 left-hand portion of the formula for p P 3? read 5?" column 4 line 55 after "tude" insert of column 6,, line 56 for geodescis read geodesics column 7 line 4L9 for "conductive" read conducive column 8 line 49 for "susbtantially' read substantially --g line 72 for tempoary read temporary column 10 line 24 for "5" read g same column lO lines 60 to 63 left hand portion of the formula for P p 21 read 211 [It Ht,

column l1 line 59 for "isolated" read isotensoid Signed and sealed this 21st day of July 1964 (SEAL) Attestz ESTON GD JOHNSON V EDWARD J, BRENNER Attesting Officer Commissioner of Patents 

1. A DEFORMABLE ISOTENSOID STRUCTURE HAVING A MULTIPLICITY OF ADJACENT PRECISELY-POSITIONED FILAMENTS HELD IN ADJACENT POSITIONS BY A COMPLIANT MATRIX MATERIAL CARRYING NO MORE THAN 10% OF THE FORCES INDUCED BY EXTERNAL LOADS, THE FILAMENTS CARRYING AT LEAST 90% OF ANY FORCES INDUCED BY EXTERNAL LOADS APPLIED TO THE STRUCTURE, THE COMPLIANCY OF SAID MATRIX MATERIAL PERMITTING SMALL CHANGES IN THE POSITION OF SAID FILAMENTS RELATIVE TO EACH OTHER, SAID STRUCTURE HAVING FILAMENTS OF A GEOMETRICAL CONFIGURATION $ RELATED TO A VOLUMETRIC LOAD VECTOR P'', REPRESENTING THE LOAD FROM EXTERNAL FORCES APPLIED TO A UNIT VOLUME OF THE STRUCTURE, BY SUBSTANTIALLY THE EQUATION: 